If a softball is hit with an upward velocity of 128 feet per second when t=0, from a height of 5 feet. (a) Find the function that models the height of the ball as a function of time. (b) Find the maximum height of the ball. (a) The function that models the height of the ball as a function of time is y= (Type an expression using t as the variable. Do not factor.)

A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call the velocity and a the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively. Figure U₁(m/s) 2.0 1.5 1.0 0.5 1(s) 0 10 20 30 40 50 1 of 1 (Figure 1) is a plot of velocity versus time for a particle that travels along a straight line with a varying velocity. Refer to this plot to answer the following questions. Part A What is the initial velocity of the particle, vo? Express your answer in meters per second. ▸ View Available Hint(s) V₁ =…

An astronaut on the Moon (g=1.62 m/s2) throws a rock from the ground level with a speed of 32.1 km/h directly upwards. Determine the time after which the rock reaches the height equal to three quarters of its maximum height on the way down.Provide your answer with the precision of two places after the decimal.

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Consider a grey squirrel falling from a tree to the ground. Use a coordinate system in which positive is downward for this problem. a) Find the squirrel’s velocity, in meters per second, just before hitting the ground when it falls from a height of 1.3 m. Ignore air resistance.  b) The squirrel softens its landing by bending its legs when it touches the ground, thereby stopping itself over a distance of 7.6 cm. Assuming a constant rate of deceleration, find the squirrel’s acceleration during this process, in meters per second squared.

You attach a meter stick to an oak tree, such that the top of the meter stick is 2.672.67 meters above the ground. Later, an acorn falls from somewhere higher up in the tree. If the acorn takes 0.1860.186 seconds to pass the length of the meter stick, how high ℎ0h0 above the ground was the acorn before it fell, assuming that the acorn did not run into any branches or leaves on the way down?

A fireworks rocket explodes at a height of 42.0 m , producing fragments with velocities ranging from 8.68 m/s downward to 16.7 m/s upward. Over what time interval are fragments hitting the ground?             Needs Complete solution with 100 % accuracy.

1) The position function of a particle is given by s = t³ - 12t² + 36t; t≥ 0. (s is measured in meters and t is measured in seconds.) (a) Find the velocity and acceleration functions. Clearly label your answers and units. (b) When is the particle at rest? Use appropriate units. (c) When is the particle moving forward? Explain/show work to receive full credit. (d) Find the acceleration when the particle reaches a velocity of 36 m/s? Use appropriate units.

A boxer's fist and glove have a mass of m = 1.04 kg. The boxer's fist can obtain a speed of v = 9.25 m/s in a time of t = 0.21 s. Write a symbolic expression for the magnitude of the average acceleration, aave, of the boxer's fist, in terms of the variables provided.  Find the magnitude of the average acceleration, aave, in meters per square second. Write an expression for the magnitude of the average net force, Fb, that the boxer must apply to his fist to achieve the given velocity. (Write the expression in terms of m, v and t.) What is the numerical value of Fb, in newtons?

A silver dollar is dropped from the top of a building that is 1345 feet tall. Use the position function below for free-falling objects. s(t) = -16t2 + vot + so (a) Determine the position and velocity functions for the coin. s(t) = v(t) = (b) Determine the average velocity on the interval [1, 2]. ft/s (c) Find the instantaneous velocities when t = 1 second and t = 2 seconds. v(1) = ft/s v(2) = ft/s (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/s